Combining and Representing Logical Systems Using Model-Theoretic Parchments

. The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. We adopt the model-theoretic view of logic as captured in the notions of institution and of parchment (an algebraic way of presenting institutions). We propose a new, modified notion of parchment together with parchment morphisms and representations. In contrast to the original parchment definition and our earlier work, in model-theoretic parchments introduced here the universal semantic structure is distributed over individual signatures and models. We lift formal properties of the categories of institutions and their representations to this level: the category of model-theoretic parchments is complete, and their representations may be put together using categorical limits as well. However, model-theoretic parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessar..